Intro Complex Analysis Lec 30, Laurent Series Calculations, Visualize Convergence on Mathematica

Lecture 30. (0:00) Lecture plan and the coming weeks. (1:33) Taylor series for f(z) = z/(z^2 + z -12) centered at z = 0 (which will also be the Laurent series centered at the same point) via partial fraction expansion and addition of Taylor series. (16:50) Check answer with "Series" on Mathematica. (24:30) Find the Laurent series centered at z = 0 in the annulus between the circles of radius 3 and 4. (31:43) Use Plot3D and Manipulate on Mathematica to visualize the modulus of f(z) and the modulus of partial sums of the Laurent series. (49:48) The order of a pole of a complex analysis function. We will relate these topics to integrals.

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